CO28 Python Script.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_lattice(m):\n",
    "    '''\n",
    "    Generates an m x m array, where each element is (pseudo)randomly assigned a value of either 1 or -1. The array is\n",
    "    thus a simulation of an m x m lattice with a (pseudo)randomly determined configuration of +1 spins and -1 spins. \n",
    "    '''\n",
    "    lattice = np.random.choice([1,-1], size=(m,m))\n",
    "    return lattice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sweep(S, J_kT, B_kT):\n",
    "    '''\n",
    "    Outputs an m x m array representing the subsequent configuration of the spins after one 'sweep' across the \n",
    "    inputted array S_init. A 'sweep' is the process of flipping or not flipping the spin of every array element, \n",
    "    with the decision to flip or not to flip being based on the Metropolis-Hastings algorithm. J_kT = J/(k_B*T), \n",
    "    and B_kT = B/(k_B*T).\n",
    "    '''\n",
    "    m = S.shape[0]\n",
    "    list_randomrowindices = np.random.choice(m, m, replace=False).tolist()\n",
    "    list_randomcolumnindices = np.random.choice(m, m, replace=False).tolist()\n",
    "    \n",
    "    for i in list_randomrowindices:\n",
    "        for j in list_randomcolumnindices:\n",
    "            s = S[i,j] #pick a random element from S_init (without replacement).\n",
    "            neighbour_sum = S[i,(j+1)%m] + S[i,(j-1)%m] + S[(i+1)%m,j] + S[(i-1)%m,j] #compute sum of immediately\n",
    "            #...neighbouring spins. The modulo operations help impose the periodic boundary conditions, which say that\n",
    "            #...for any particular row/column in the array, its first element would be a neighbour of its last element,\n",
    "            #...and vice versa. We can visualise how this works by imagining the array as a 2D sheet and folding it into\n",
    "            #...a torus.\n",
    "            delta_E_kT = J_kT*2*s*neighbour_sum + B_kT*2*s #compute change in (effective) energy. The factor of 2 exists\n",
    "            #...because if s were flipped, the magnitude of the change in energy would be equal to twice the initial energy.\n",
    "            if delta_E_kT <= 0:\n",
    "                s *= -1\n",
    "            elif np.random.rand() < np.exp(-delta_E_kT):\n",
    "                s *= -1\n",
    "            S[i,j] = s\n",
    "    return S.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_magnetic_moment(S):\n",
    "    '''\n",
    "    Calculates the magnetic moment.\n",
    "    '''\n",
    "    return np.sum(S)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_critical_value(x_list, y_list):\n",
    "    '''\n",
    "    Returns the value in x_list corresponding to the value in y_list for which the sum of the differences between itself \n",
    "    and its nearest-neighbouring values is the greatest.\n",
    "    '''\n",
    "    y_diff_list = []\n",
    "    y_index_max = len(y_list)-1\n",
    "    y_index_list = list(range(1,y_index_max))\n",
    "    for y_index in y_index_list:\n",
    "        y_diff = y_list[y_index+1] - y_list[y_index-1]\n",
    "        y_diff_list.append(y_diff)\n",
    "    y_diff_max = max(y_diff_list)\n",
    "    y_diff_max_index = y_diff_list.index(y_diff_max)\n",
    "    critical_value_index = y_index_list[y_diff_max_index]\n",
    "    critical_value = x_list[critical_value_index]\n",
    "    return critical_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_configuration(state, sweep_count):\n",
    "    '''\n",
    "    Produces a colour map representing the configuration (lattice) of spins. Saves the colour map to /Pictures folder. \n",
    "    '''\n",
    "    plt.figure(figsize=(7, 7), dpi=100)\n",
    "    plt.imshow(state, cmap=plt.cm.get_cmap('jet', 2), origin='lower')\n",
    "    plt.colorbar(ticks=[-1,0,1], label='Spin', extend='both')\n",
    "    plt.title('Configuration after sweep number {}'.format(sweep_count), fontsize=17)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_data(x_list, y_list, title_str, x_label_str, y_label_str):\n",
    "    '''\n",
    "    Plots y_list (list of values for dependent variable) against x_list (list of values for independent variable). \n",
    "    '''\n",
    "    plt.figure(figsize=(7, 7), dpi=100)\n",
    "    plt.plot(x_list, y_list, 'bo', markersize=2)\n",
    "    plt.title(title_str, fontsize=17)\n",
    "    plt.xlabel(x_label_str, fontsize=14)\n",
    "    plt.ylabel(y_label_str, fontsize=14)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_special_data(x_list, y_list, title_str, x_label_str, y_label_str):\n",
    "    '''\n",
    "    Plots y_list (list of values for dependent variable) against x_list (list of values for independent variable).\n",
    "    This module is specially for plotting M against J/(k_B*T).\n",
    "    '''\n",
    "    plt.figure(figsize=(7, 7), dpi=100)\n",
    "    plt.plot(x_list, y_list, 'bo', markersize=2)\n",
    "    plt.axvline(x=0.44, linewidth=1, color='r', alpha=0.8)\n",
    "    plt.axvline(x=get_critical_value(x_list, y_list), linewidth=1, color='g', alpha=0.8)\n",
    "    plt.title(title_str, fontsize=17)\n",
    "    plt.xlabel(x_label_str, fontsize=14)\n",
    "    plt.ylabel(y_label_str, fontsize=14)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def overlay_plot_with_errorbars(x_list, y_list, y_error_list, title_str, x_label_str, y_label_str):\n",
    "    '''\n",
    "    Overlay of plot of y_list (list of values for dependent variable) against x_list (list of values for independent... \n",
    "    variable) and plot of analytically-derived relation between M and J/(k_B*T).\n",
    "    This module is specially for a particular plot of M against J/(k_B*T), with error bars included.\n",
    "    '''\n",
    "    plt.figure(figsize=(7, 7), dpi=100)\n",
    "    plt.plot(x_list, y_list, 'bo', markersize=2, label='Computational Result')\n",
    "    plt.errorbar(x_list, y_list, yerr=y_error_list, fmt='bo', markersize=2, color='blue', ecolor='blue', elinewidth=1, capsize=3)\n",
    "    input_list = [i * 2 for i in x_list]\n",
    "    M_list = (1 - (np.sinh(input_list))**(-4))**(1/8)\n",
    "    plt.plot(x_list, M_list, 'ro', markersize=2, label='Analytical Result')\n",
    "    plt.title(title_str, fontsize=17)\n",
    "    plt.xlabel(x_label_str, fontsize=14)\n",
    "    plt.ylabel(y_label_str, fontsize=14)\n",
    "    plt.legend(loc='lower right')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def run_simulation(S_0, J_kT, B_kT, sweep_total):\n",
    "    '''\n",
    "    Performs the simulation by sweeping across an initial lattice S_0 a number of times (number = sweep_total). \n",
    "    Returns a list of relevant values (e.g., the stabilised magnetisation). \n",
    "    '''\n",
    "    M_list = []\n",
    "    M_abs_list = []\n",
    "    M_cumulative_list = []\n",
    "    sweep_count_list = []\n",
    "    S_colormap_list = []\n",
    "    colormap_sweep_count_list = []\n",
    "\n",
    "    \n",
    "    # To avoid effect of initial state\n",
    "    for count in range(50):\n",
    "        S_init = sweep(S_0, J_kT, B_kT)\n",
    "\n",
    "\n",
    "    # Start proper sweep\n",
    "    for sweep_count in range(sweep_total + 1):\n",
    "        S_next = sweep(S_init, J_kT, B_kT)\n",
    "        S_init = S_next\n",
    "        M = calc_magnetic_moment(S_next)\n",
    "        M_list.append(M)\n",
    "        M_cumulative_list.append(sum(M_list))\n",
    "        M_abs = abs(M)\n",
    "        M_abs_list.append(M_abs)\n",
    "        sweep_count_list.append(sweep_count)\n",
    "    \n",
    "        if (sweep_count) % (sweep_total/8) == 0:\n",
    "        # Extract S_next at 8 different stages to plot the color maps later\n",
    "            S_colormap_list.append(S_next)\n",
    "            colormap_sweep_count_list.append(sweep_count)\n",
    "   \n",
    "\n",
    "    # Obtain a list of |M| values from the 500th sweep till the last sweep. |M| is assumed to have reached a stable value by\n",
    "    #...the 500th sweep; we make this supposition based on prior plots of |M| against sweep number for different values of \n",
    "    #...J/k_BT and B/k_BT.\n",
    "    stable_M_abs_histogram_data = M_abs_list[500:]\n",
    "\n",
    "    # Fit a normal distribution to the list of values of |M|, and compute the mean and standard deviation. \n",
    "    mu, std = norm.fit(stable_M_abs_histogram_data)\n",
    "    \n",
    "    return [mu, std, M_list, M_cumulative_list, M_abs_list, sweep_count_list, S_colormap_list, colormap_sweep_count_list]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Import relevant libraries\n",
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import rc\n",
    "\n",
    "rc('text', usetex=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\richa\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:11: RuntimeWarning: invalid value encountered in power\n",
      "  # This is added back by InteractiveShellApp.init_path()\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Initialise variables\n",
    "S_0 = create_lattice(30)\n",
    "B_kT = 0 # try the following values of B_kT: 0, 0.001, 0.01\n",
    "J_kT_list = np.arange(0.44, 1.01, 0.005).tolist()\n",
    "sweep_total = 2000\n",
    "stable_M_abs_normalised_mean_list = []\n",
    "stable_M_abs_normalised_mean_error_list = []\n",
    "\n",
    "\n",
    "# Obtain lists of magnetisation values and their standard deviations for different values of J/(k_B*T)\n",
    "for J_kT in J_kT_list:\n",
    "    list_relevantvalues = run_simulation(S_0, J_kT, B_kT, sweep_total)\n",
    "    magnetisation = list_relevantvalues[0]\n",
    "    magnetisation_error = list_relevantvalues[1]\n",
    "    stable_M_abs_normalised_mean_list.append(magnetisation/900)\n",
    "    stable_M_abs_normalised_mean_error_list.append(magnetisation_error/900)\n",
    "\n",
    "\n",
    "# Output overlay of plots of analytical and computational results for stable magnetic moment against J/(k_B*T)\n",
    "overlay_plot_with_errorbars(J_kT_list, stable_M_abs_normalised_mean_list, stable_M_abs_normalised_mean_error_list, \"Stabilised $|M|_{\\small \\mbox{normalised}}$ against $J/k_BT$ $\\hspace{5mm}$(for $B=0$)\", \"$J/k_BT$\", \"Stabilised $|M|_{\\small \\mbox{normalised}}$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The estimated critical value of J/(k_B*T) at which phase transition occurs is: 0.425\n"
     ]
    }
   ],
   "source": [
    "# Initialise variables\n",
    "S_0 = create_lattice(30)\n",
    "B_kT = 0 # try the following values of B_kT: 0, 0.001, 0.01\n",
    "J_kT_list = np.arange(0, 1.01, 0.005).tolist()\n",
    "sweep_total = 2000\n",
    "stable_M_abs_mean_list = []\n",
    "\n",
    "\n",
    "# Obtain a list of magnetisation values for different values of J/(k_B*T)\n",
    "for J_kT in J_kT_list:\n",
    "    list_relevantvalues = run_simulation(S_0, J_kT, B_kT, sweep_total)\n",
    "    magnetisation = list_relevantvalues[0]\n",
    "    stable_M_abs_mean_list.append(magnetisation)\n",
    "    \n",
    "\n",
    "# Output plot of stable magnetic moment against J/(k_B*T). \n",
    "# red, vertical line marks out the analytically derived critical value of J/(k_B*T) ~ 0.44 (when B = 0).\n",
    "# The green, vertical line provides a (rough) indication of where the phase transition might have occurred.\n",
    "plot_special_data(J_kT_list, stable_M_abs_mean_list, \"$|M|_{\\small \\mbox{stable}}$ against $J/k_BT$ $\\hspace{5mm}$(for $B=0$)\", \"$J/k_BT$\", \"$|M|_{\\small \\mbox{stable}}$\")\n",
    "\n",
    "\n",
    "# Print (approximate) critical value for the phase transition. Corresponds to green, vertical line.\n",
    "Critical_Value = get_critical_value(J_kT_list, stable_M_abs_mean_list)\n",
    "print(\"The estimated critical value of J/(k_B*T) at which phase transition occurs is: \" + str(Critical_Value))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The estimated critical value of J/(k_B*T) at which phase transition occurs is: 0.42\n"
     ]
    }
   ],
   "source": [
    "# Initialise variables\n",
    "S_0 = create_lattice(30)\n",
    "B_kT = 0.001 # try the following values of B_kT: 0, 0.001, 0.01\n",
    "J_kT_list = np.arange(0, 1.01, 0.005).tolist()\n",
    "sweep_total = 2000\n",
    "stable_M_abs_mean_list = []\n",
    "\n",
    "\n",
    "# Obtain a list of magnetisation values for different values of J/(k_B*T)\n",
    "for J_kT in J_kT_list:\n",
    "    list_relevantvalues = run_simulation(S_0, J_kT, B_kT, sweep_total)\n",
    "    magnetisation = list_relevantvalues[0]\n",
    "    stable_M_abs_mean_list.append(magnetisation)\n",
    "    \n",
    "\n",
    "# Output plot of stable magnetic moment against J/(k_B*T). \n",
    "#The red, vertical line marks out the analytically derived critical value of J/(k_B*T) ~ 0.44 (when B = 0).\n",
    "#The green, vertical line provides a (rough) indication of where the phase transition might have occurred.\n",
    "plot_special_data(J_kT_list, stable_M_abs_mean_list, \"$|M|_{\\small \\mbox{stable}}$ against $J/k_BT$ $\\hspace{5mm}$(for $B=0.001$)\", \"$J/k_BT$\", \"$|M|_{\\small \\mbox{stable}}$\")\n",
    "\n",
    "\n",
    "# Print (approximate) critical value for the phase transition. Corresponds to green, vertical line.\n",
    "Critical_Value = get_critical_value(J_kT_list, stable_M_abs_mean_list)\n",
    "print(\"The estimated critical value of J/(k_B*T) at which phase transition occurs is: \" + str(Critical_Value))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The estimated critical value of J/(k_B*T) at which phase transition occurs is: 0.41000000000000003\n"
     ]
    }
   ],
   "source": [
    "# Initialise variables\n",
    "S_0 = create_lattice(30)\n",
    "B_kT = 0.01 # try the following values of B_kT: 0, 0.001, 0.01\n",
    "J_kT_list = np.arange(0, 1.01, 0.005).tolist()\n",
    "sweep_total = 2000\n",
    "stable_M_abs_mean_list = []\n",
    "\n",
    "\n",
    "# Obtain a list of magnetisation values for different values of J/(k_B*T)\n",
    "for J_kT in J_kT_list:\n",
    "    list_relevantvalues = run_simulation(S_0, J_kT, B_kT, sweep_total)\n",
    "    magnetisation = list_relevantvalues[0]\n",
    "    stable_M_abs_mean_list.append(magnetisation)\n",
    "    \n",
    "\n",
    "# Output plot of stable magnetic moment against J/(k_B*T). \n",
    "#The red, vertical line marks out the analytically derived critical value of J/(k_B*T) ~ 0.44 (when B = 0).\n",
    "#The green, vertical line provides a (rough) indication of where the phase transition might have occurred.\n",
    "plot_special_data(J_kT_list, stable_M_abs_mean_list, \"$|M|_{\\small \\mbox{stable}}$ against $J/k_BT$ $\\hspace{5mm}$(for $B=0.01$)\", \"$J/k_BT$\", \"$|M|_{\\small \\mbox{stable}}$\")\n",
    "\n",
    "\n",
    "# Print (approximate) critical value for the phase transition. Corresponds to green, vertical line.\n",
    "Critical_Value = get_critical_value(J_kT_list, stable_M_abs_mean_list)\n",
    "print(\"The estimated critical value of J/(k_B*T) at which phase transition occurs is: \" + str(Critical_Value))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "scrolled": true
   },
   "outputs": [],
   "source": [
    "# Initialise variables\n",
    "S_0 = create_lattice(30)\n",
    "B_kT = 0 # try any of the following values of B_kT: 0, 0.001, 0.01\n",
    "J_kT = 0.65 # try any value between 0 and 1 (inclusive)\n",
    "sweep_total = 1000\n",
    "\n",
    "# Run simulation for selected values (above) and obtain relevant data\n",
    "list_relevantvalues = run_simulation(S_0, J_kT, B_kT, sweep_total)\n",
    "[mu, std, M_list, M_cumulative_list, M_abs_list, sweep_count_list, S_colormap_list, colormap_sweep_count_list] = list_relevantvalues"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 18 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Output color maps\n",
    "fig = plt.figure(figsize=(12, 12), dpi = 120)\n",
    "columns = 3\n",
    "rows = 3\n",
    "for i in range(1, columns*rows + 1):\n",
    "    state = S_colormap_list[i-1]\n",
    "    fig.add_subplot(rows, columns, i)\n",
    "    plt.imshow(state, cmap=plt.cm.get_cmap('jet', 2), origin='lower')\n",
    "    colormap_sweep_count = colormap_sweep_count_list[i-1]\n",
    "    plt.title('Configuration after {} sweeps'.format(colormap_sweep_count))\n",
    "    plt.colorbar(ticks=[-1,0,1], label='Spin', extend='both')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Output plot of magnetic moment M against sweep count\n",
    "plot_data(sweep_count_list, M_list, \"$M$ against Sweep Count\", \"Sweep count\", r\"$M$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Output plot of normalised magnetic moment M/M_max against sweep count\n",
    "M_normalised_list = [i/900 for i in M_list]\n",
    "plot_data(sweep_count_list, M_normalised_list, \"$M_{\\small \\mbox{normalised}}$ against Sweep Count\", \"Sweep count\", r\"$M_{\\small \\mbox{normalised}}$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Output plot of absolute value of magnetic moment |M| against sweep count\n",
    "plot_data(sweep_count_list, M_abs_list, \"$|M|$ against Sweep Count\", \"Sweep count\", r\"$|M|$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Output plot of normalised absolute value of magnetic moment |M|/|M|_max against sweep count\n",
    "M_abs_normalised_list = [i/900 for i in M_abs_list]\n",
    "plot_data(sweep_count_list, M_abs_normalised_list, \"$|M|_{\\small \\mbox{normalised}}$ against Sweep Count\", \"Sweep count\", r\"$|M|_{\\small \\mbox{normalised}}$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Output plot of cumulative magnetic moment M_cumulative against sweep count\n",
    "plot_data(sweep_count_list, M_cumulative_list, \"$M_{\\small \\mbox{cumulative}}$ against Sweep Count\", \"Sweep count\", r\"$M_{\\small \\mbox{cumulative}}$\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 700x700 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plots the distribution of (stabilised) magnetisation values. Just for visualisation purposes.\n",
    "\n",
    "\n",
    "M_abs_normalised_mean_list = []\n",
    "\n",
    "# Obtain a list of |M| values from the 500th sweep till the last sweep. |M| is assumed to have reached a stable value by\n",
    "#...the 500th sweep; we make this supposition based on prior plots of |M| against sweep number for different values of \n",
    "#...J/k_BT and B/k_BT. Of course, the number can be changed on discretion.\n",
    "M_abs_normalised_histogram_data = M_abs_normalised_list[500:]\n",
    "\n",
    "# Fit a normal distribution to the list of values of |M|, and compute the mean and standard deviation. \n",
    "mu, std = norm.fit(M_abs_normalised_histogram_data)\n",
    "\n",
    "# Save the value of the mean.\n",
    "M_abs_normalised_mean_list.append(mu)\n",
    "\n",
    "# Set the size of the plot.\n",
    "plt.figure(figsize=(7, 7), dpi=100)\n",
    "\n",
    "# Plot the histogram.\n",
    "plt.hist(M_abs_normalised_histogram_data, bins=20, density=True, alpha=0.6, color='g')\n",
    "\n",
    "# Plot the PDF.\n",
    "xmin, xmax = plt.xlim()\n",
    "x = np.linspace(xmin, xmax, 100)\n",
    "p = norm.pdf(x, mu, std)\n",
    "plt.plot(x, p, 'k', linewidth=2)\n",
    "plt.xlabel('Stabilised Magnetisation (normalised)', fontsize = 14)\n",
    "plt.ylabel('Frequency', fontsize = 14)\n",
    "title = \"Fit results: $\\mu$ = %.3f,  $\\sigma$ = %.3f\" % (mu, std)\n",
    "plt.title(title, fontsize = 17)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}